High-resolution volumetric imaging constrains compartmental models to explore synaptic integration and temporal processing by cochlear nucleus globular bushy cells

Globular bushy cells (GBCs) of the cochlear nucleus play central roles in the temporal processing of sound. Despite investigation over many decades, fundamental questions remain about their dendrite structure, afferent innervation, and integration of synaptic inputs. Here, we use volume electron microscopy (EM) of the mouse cochlear nucleus to construct synaptic maps that precisely specify convergence ratios and synaptic weights for auditory nerve innervation and accurate surface areas of all postsynaptic compartments. Detailed biophysically based compartmental models can help develop hypotheses regarding how GBCs integrate inputs to yield their recorded responses to sound. We established a pipeline to export a precise reconstruction of auditory nerve axons and their endbulb terminals together with high-resolution dendrite, soma, and axon reconstructions into biophysically detailed compartmental models that could be activated by a standard cochlear transduction model. With these constraints, the models predict auditory nerve input profiles whereby all endbulbs onto a GBC are subthreshold (coincidence detection mode), or one or two inputs are suprathreshold (mixed mode). The models also predict the relative importance of dendrite geometry, soma size, and axon initial segment length in setting action potential threshold and generating heterogeneity in sound-evoked responses, and thereby propose mechanisms by which GBCs may homeostatically adjust their excitability. Volume EM also reveals new dendritic structures and dendrites that lack innervation. This framework defines a pathway from subcellular morphology to synaptic connectivity, and facilitates investigation into the roles of specific cellular features in sound encoding. We also clarify the need for new experimental measurements to provide missing cellular parameters, and predict responses to sound for further in vivo studies, thereby serving as a template for investigation of other neuron classes.

. The imaged volume in the cochlear nucleus captures globular bushy (GBC) and multipolar cells (MC), and reveals synaptic sites. (A) The VCN region that was imaged using SBEM is depicted within walls of the image volume. Twenty-six GBCs (beige) and 5 MCs (orange) are shown with their axons (red). Left rear wall transects auditory nerve (anf) fascicles, which run parallel to the right rear wall and floor. Non-anf axons exit into the right rear wall and floor as part of other fascicles that are cross-sectioned. The complete volume can be viewed at low resolution in Figure 1-video 1. (B) Example image, cropped from the full field of view, from the data set in panel A. Field of four GBC (bc) cell bodies, myelinated axons in anf fiber fascicles, and capillaries (c). (C) Closeup of the cell body (cb) of lower right GBC from panel B, illustrating the eccentrically located nucleus (n), short stacks of endoplasmic reticulum (er) aligned with the cytoplasm-facing side of the nuclear envelope, and contact by an endbulb (eb). (D) Closeup of the labeled endbulb contacting the cell in panel C (eb), revealing its initial expansion along the cell surface. Apposed pre-and postsynaptic surface area (ASA; green) are accurately determined by excluding regions with intercellular space (ASA is discontinuous), and synaptic sites (s1-4) are indicated as clusters of vesicles with some contacting the presynaptic membrane. (D') Inset in panel D is closeup of synapse at lower left in panel D. It shows defining features of synapses in these SBEM images, which include clustering of vesicles near the presynaptic membrane, convex shape of the postsynaptic membrane, and in many cases a narrow band of electron-dense material just under the membrane, as evident here between the "s1" symbol and the postsynaptic membrane.Green line indicates regions of directly apposed pre-and postsynaptic membrane, and how this metric can be accurately quantified using EM. (E) Histogram of all somatic surface areas generated from computational meshes of the segmentation. GBCs are denoted with grey bars and MCs with red bars. (F) Synapse density plotted against ASA shows a weak negative correlation. Marginal histogram of density values is plotted along the ordinate. Scale bars = 5 in B, 2 in C, 1 in D, 250 nm in D'.  Exploration of the relation between an image volume and a globular bushy cell (GBC) mesh derived from that volume. This video opens with a top-down view of the SBEM image volume from the ventral cochlear nucleus. The video zooms in as the volume is slowly cut away to reveal GBC05, including its dendrites (red), cell body (beige), axon (pink), and all large somatic inputs (various colors). The perspective then shifts laterally to view several of the large terminals (various colors) contacting the cell body.      Figure 2B. 183 Innervation of globular bushy cells shows specificity for auditory nerve fiber fasci-184 cles 185 The majority (98/158) of end bulbs could be traced along axon branches to parent ANFs consti-186 tuting fascicles within the image volume. The remaining branches exited the volume (2/6 and 187 3/8 branches (white arrowheads), respectively, for example cells in Figure 3 A, B). We then asked 188 whether the fascicle organization of the auditory nerve fibers was related to innervation patterns, 189 whereby most inputs to a particular cell might be associated with the same fascicle. We identi-  (Figure 3A,B). Excluding 4 cells near the edge of the image volume (GBCs 02, 24,29,195 14 plotted at left in right histogram of Figure 3C), 2-9 endbulbs from individual cells were traced to 196 ANFs in the same major fascicle (for the example cells in Figure 3A,B, 2 fascicles each contained 2 197 parent axons of inputs to each cell (fascicles #2, #3, and #2, #7, respectively)). None of the parent 198 ANFs that were linked to endbulbs branched more than once within the volume. The proportion of 199 axons yielding endbulb terminals within the image volume was low in some fascicles (fasicles #3, 200 #4, #5, #6; fasicle #4 contributed no endbulbs), and high in others (#1, #7; GBC08 had 9 endbulbs 201 traced to fascicle #7). These observations indicate that the auditory nerve fascicles preferentially 202 innervated different rostro-caudal territories of the same frequency region (Figure 3D). 203 The myelinated lengths of branches from parent fibers to terminals varied from 0 (endbulbs 204 emerged en passant from parent terminal in two cases) to 133 ( Figure 3G). For a subset of 205 10 GBCs with at least 4 branches traced back to parent ANFs, we utilized the resolution and ad-206 vantages of volume EM to assay axon morphology. Branches were thinner than the parent ANFs, 207 (1.4 (SD 0.33) vs 2.7 (SD 0.30) diameter), and both the parent ANF and branches had the same   Figure 3-video 1 for a detailed 3-D view of GBC11 and its inputs. Figure 3-video 1. Exploration of all large somatic inputs onto a single globular bushy cell (GBC), their branch axons, and parent auditory nerve fibers. This video opens with a full view of GBC11, including its dendrites (red), cell body (beige), axon (pink), all of its large somatic inputs (various colors), and the auditory nerve fibers (ANFs) from which those inputs originate. Somatic inputs and their axon branches, including the parent ANF, share the same color. The view zooms into the cell body, where a large terminal (red) extends onto the axon hillock and initial segment (blue arrow). The view pans around the cell body to show all large terminals, and an axon (cyan) that exited the volume before likely linking to an ANF is indicated by a red arrow. All except two terminals are then removed. The axons of these terminals are traced to branch points from their parent ANFs (magenta arrows). All inputs and their axons are replaced, and a second axon (green) that exits the volume before likely linking to an ANF is indicated (red arrow). The view pans to two ANFs (red and yellow) from the same nerve fascicle, and their branch points (magenta arrows). All other nerve terminals and axons are removed, and the two branch axons are traced to the cell body.

Passive
Half-active Active GBC17 CNModel Channel Decorator g leak g KLT   The mesh representation of the volume EM segmentation was traced using syGlass virtual reality software to generate an SWC file consisting of locations, radii, and the identity of cell parts (B). In (B), the myelinated axon is dark red, the axon initial segment is light blue, the axon hillock is red, the soma is black, the primary dendrite is purple, dendritic hubs are blue, the secondary dendrite is dark magenta, and the swellings are gold. The mesh reconstruction and SWC reconstructions are shown from different viewpoints. See Comparison of responses to current pulses ranging from -1 to + 2 nA for each dendrite decoration scheme. In the Passive scheme, the dendrites contain only leak channels; in the Active scheme, the dendrites are uniformly decorated with the same density of channels as in the soma. In the Half-active scheme, the dendritic channel density is one-half that of the soma. (E) Current voltage relationships for the 3 different decoration schemes shown in (D). Curves indicated with circles correspond to the peak voltage (exclusive of APs); curves indicated with squares correspond to the steady state voltage during the last 10 ms of the current step.      This video opens with a full side-by side views of the GBC11 reconstruction (left), including its dendrites (red), cell body (beige), and axon (pink), and the SWC representation (right) of the same structures. The view then zooms into the cell body and axon, where the transition point from cell body to the axon (yellow arrow), the middle of the unmyelinated initial segment (green arrow), and the transition point where myelination of the axon begins (blue arrow) are indicated. Note that the diameter of the axon increases significantly where it is myelinated. Location of last paranodal loop of myelin is indicated by narrow, peach-colored band to right of the blue arrow on the SWC representation. The view then pans to a dorsolateral view of the cell, where a pink arrow indicates the proximal dendrite, and an orange arrow signifies the primary hub of the cell. The view then pans to a top-down location showing two secondary hubs (orange arrows). The view then shifts to reveal periodic dendrite swellings (three cyan arrows) separated by dendrite shafts (two red arrows). SWC color code: pink, cell body; axon hillock, orange; axon initial segment, light green; myelinated axon, light blue; proximal dendrite, maroon; dendrite hub, greenish-brown; dendrite swelling, cyan; dendrite shaft, gray. The wide variation in size of the endbulb inputs ( Figure 2C-F) suggests that inputs with a range of 283 synaptic strengths converge onto the GBCs. We then inquired whether individual cells followed 284 the coincidence-detection or mixed-mode models hypothesized by input sizes shown in Figure 2D. 285 To address this question, we first modeled the responses by each of the 10 fully reconstructed  Without specific knowledge of the spontaneous rate or a justifiable morphological proxy measure, 291 we modeled all ANFs as having high spontaneous rates since this group delivers the most contacts 292 to GBCs in cat ( Fig.9 in Liberman, 1991). 293 We chose four cells to illustrate the range of model responses. GBC05 and GBC30 ( Figure 5A1,  The second largest input for GBC09 (132 ) had higher efficacy than the largest input for 302 GBC30 (172 ). The variation of efficacy for similar ASA was evident, especially between 125-175 303 , in a plot of all inputs across the ten GBCs ( Figure 5D). Since many cells lacked inputs in this  , and 17 formed one group, and GBCs 02, 05, 06, 10, 13 18, and 30 formed a second group with overall lower efficacy. The red line is a best fit logistic function to the higher efficacy group. The blue dashed line is the logistic fit to the lower efficacy group. Stars indicate test ASA-efficacy points, supporting membership in the lower efficacy group for cells 10 and 30. Although GBC13 had a single large input, its smaller AN inputs grouped with the lower efficacy group. (E) Comparison of the patterns of individual inputs that generate spikes. Ordinate: 1 + indicates spikes driven by the largest input plus any other inputs. 2 + indicates spikes driven by the second largest input plus any smaller inputs, excluding spikes in which the largest input was active. 3 + indicates spikes driven by the third largest input plus any smaller inputs, but not the first and second largest inputs. 4 ℎ + indicates contributions from the fourth largest input plus any smaller inputs, but not the 3 largest. 5 ℎ + indicates contributions from the fifth largest input plus any smaller inputs, but not the 4 largest. Colors and symbols are coded to individual cells, here grouped according to predicted coincidence mode or mixed-mode input patterns as shown in Figure2   (likely because GBC17 has two suprathreshold inputs), all subthreshold inputs had appreciable co-340 incidence rates. The summation of inputs to generate many of the APs for GBC09 is seen in the 341 voltage traces preceding spikes, but most APs for GBC17 emerge rapidly without a clear preceding 342 EPSP ( Figure 5C3, C4, respectively).

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To understand how weaker inputs contributed independently of the largest inputs, we also 344 calculated the fraction of postsynaptic spikes that were generated without the participation of si-345 multaneous spikes from the N larger inputs (where N varied from 1 to number of inputs -1, thus 346 successively peeling away spikes generated by the larger inputs). We focused initially on mixed-347 mode cells ( Figure 5E). We first calculated the fraction of postsynaptic spikes generated by the 348 largest input in any combination with other inputs (in the time window -2.7 to -0.5 ms relative to 349 the spike peak as in Figure 5B). This fraction ranged from 40-60% in mixed-mode cells (hexagons, 350 1 + in Figure 4E). The fraction of postsynaptic spikes generated by the second-largest input in 351 any combination with other smaller inputs was surprisingly large, ranging from 25-30% (excluding 352 GBC17 which had 2 suprathreshold inputs; 2 + in Figure 5E). Notably, all combinations of inputs For GBCs that are predicted to operate in the coincidence-detection mode, we hypothesized 358 that the contributions of different sized inputs would be more uniform. We tested this using tone 359 stimuli at 30dB SPL. Surprisingly, in two of the cells with the largest inputs (GBC02, GBC30), the 360 largest input in combination with all of the smaller inputs (circles, 1 + in Figure 5E) accounted larger inputs can have a disproportional influence that equals or exceeds that of suprathreshold 367 inputs in mixed-mode cells. 368 We next inquired whether the participation of weak inputs in AP generation depended on stim-369 ulus intensity (spontaneous activity at 0 dB SPL and driven activity at 30 dB SPL), or was normalized 370 by the increase in postsynaptic firing rate. To address this question, we computed a participation 371 metric for each endbulb as #postsynaptic APs for which a presynaptic AP from a given input oc-372 curred in the integration window (-2.7 to -0.5 ms relative to the spike peak), divided by the total 373 number of #postsynaptic APs. The smaller inputs have a higher relative participation at 30 dB 374 SPL than larger inputs (Figure 5F), suggesting a rate-based increase in coincidence among weaker 375 inputs at higher intensities. This level-dependent role of smaller inputs was also explored in cumu-376 lative probability plots of the number of inputs active prior to a spike between spontaneous and 377 sound-driven ANFs. During spontaneous activity, often only one or two inputs were active prior an 378 AP ( Figure 4G, triangles). However, during tone-driven activity postsynaptic spikes were, on aver-

397
To explore contributions of cell geometry to synaptic efficacy, we plotted threshold as a function 398 of compartment surface area or length. Threshold was highly correlated with dendrite surface area 399 ( < . , = . , Figure 5I), but modestly correlated with soma surface area ( = . , = .
, 400 Figure 5J) or the ratio of dendrite to soma surface areas ( = . , = . . Taken together, 401 these simulations predict that dendrite surface area is a stronger determinant of excitability than of small inputs and suprathreshold inputs could generate spikes at different phases of modulation. 470 We hypothesized that removing the largest input and, for GBC17, the two largest inputs, would con-  Figure 6P1,P2. 485 We also computed the rate modulation transfer functions (rMTF) for each input configuration      (range 3.2 -19.6 ; 12.9 (SD 6.2) ) from the cell body. 518 We used the ten GBCs with complete or nearly complete dendrite segmentations to compute addi-

537
A complete map of synaptic inputs reveals dendrite branches that lack innervation 538 We report here the first map for locations of all synaptic terminals onto soma, dendrites and axon 539 of a GBC (GBC09; Figure 8A,B). In addition to 8 endbulb inputs from ANFs, 97 small terminals con-540 tacted the cell body. Together these inputs covered 83% of its somatic surface (Figure 8C, D). This  Notably, entire dendrite branches could be devoid of innervation (black arrows in Figure 8B), 554 and instead were wrapped by glial cells, or extended into bundles of myelinated axons (Figure 8F). 555 Even though they are not innervated, these branches will affect the passive electrical properties of 556 the cell by adding surface area. We inquired whether these dendrites constitute sufficient surface  Exploration of a globular bushy cell (GBC) and all of its synaptic inputs. This video opens with a full view of GBC09, including its dendrites (red), cell body (beige), axon (pink), all somatic inputs (various colors), and all dendritic inputs (various colors). The cell undergoes a full rotation to display all of the inputs. The view zooms into the axon region, and rotates to illustrate all inputs onto the axon, including extensions of two large terminals (blue arrows pointing to purple and yellow terminals). The view zooms out to show the entire cell, the dendrites are removed, and the cell body is tilted. A cut plane passes from the edge to the middle of the cell, providing an inside-out view of the nearly complete synaptic coverage of the cell body. Large terminals are indicated by cyan arrows. All cellular elements are added, and the view shifts to reveal dense innervation of the proximal dendrite, including an extension of a large terminal (green terminal indicated by green arrow). The perspective shifts to a top-down view of the dendrites, indicating several dendritic branches (yellow arrows) that lack synaptic inputs. 20 of 46 with the non-innervated dendrites pruned. Pruning increased the input resistance from 20.2 to 559 25.1 MΩ, (Figure 8I, J) and increased the time constant from 1.47 ms to 1.65 ms. The threshold for 560 action potential generation for short current pulses decreased from 0.439 to 0.348 nA (Figure 8J), 561 but the cell maintained its phasic firing pattern to current pulses ( Figure 8I compared to Figure   562 3- Figure Supplement 3, "Half-active"). These seemingly subtle changes in biophysical parameters 563 increased the efficacy for the 4 largest inputs (0.689 to 0.786 (14%); 0.136 to 0.431 (216%); 0.021 564 to 0.175 (733%);, 0.00092 to 0.00893 (871%); Figure 8K, L). Note that the increase was fraction-565 ally larger for the 2 nd and 3 rd largest inputs compared to the first, reflecting a ceiling effect for 566 the largest input. We also examined how pruning non-innervated dendrites is predicted to af-567 fect phase locking to SAM tones ( Figure 8M). Pruning decreased VS at 100 Hz, thereby sharpening 568 tuning to 200 Hz relative to ANFs. The rMTF (Figure 8M, inset) shows a slightly higher rate after 569 pruning of uninnervated dendrites. From these simulations, we hypothesize that GBCs can tune

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By matching inputs to a cochlear model (Zilany et al., 2014; Rudnicki et al., 2015), we created a 599 well-constrained data exploration framework that expands on previous work (Manis and Campag-600 nola, 2018). We propose that generation of compartmental models, from high-resolution images, 601 for multiple cells within a neuron class is an essential step to understand neural circuit function.

602
This approach also reveals that there are additional critical parameters, such as ion channel den-603 sities in non-somatic cellular compartments, including non-innervated dendrites, that need to be 604 measured. From these detailed models, more accurate reduced models that capture the natu- will require reconstructing longer sections of these axons to reveal regional branching patterns.  to SAM tones are qualitatively consistent with existing experimental data but this conclusion needs 678 to be experimentally tested.

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Other future enhancements to the models, by characterizing inputs by their putative excitatory  ., 2006). 725 The dynamics of dendrite branch remodeling have not, to our knowledge, been examined at high 726 temporal resolution, but are amenable to modern imaging methods such as have been applied to 727 studies of dendritic spine structural plasticity. 728 We also found that the length of the AIS, which is the spike initiation zone for most neurons 729 (Bender and Trussell, 2012), varied across GBCs by 50% (14-21 ). Changing AIS length, while 730 assuming a constant density of Na + channels, is predicted to non-linearly change rheobase by 731 50% (Figure 4K). Interestingly, the AIS of each GBC is contacted by multiple small inputs. Inhibitory  Our high-resolution images revealed a previously undescribed dendrite structure, which we name 776 a hub. The high branching order of hubs helps explain why GBC dendrites are contained locally 777 to the cell body. We also revealed that dendrites branch and align adjacent to one another. This 778 arrangement increases the surface area to volume ratio, which affects the excitability of the cell.  Resin-embedded tissue was mounted on an aluminum specimen pin (Gatan) using cyanoacrylic 832 glue and precision trimmed with a glass knife to a rectangle ≈0.5 × 0.75 mm so that tissue was oriented organelles with diameters measured in the image plane (Wilke et al., 2013). 846 A volume of 148 x 158 x 111 was imaged with an in-plane pixel resolution of 5.5 nm.  (Jackson et al., 2021). Images were assessed to be of high quality for segmentation due to well 855 preserved membranes, as evidenced also by uniform preservation of tightly wrapped myelin, and 856 the absence of degenerating profiles. measurements. Thus, we evaluated more consistent mesh processing algorithms. 905 We implemented accurate mesh processing by applying the GAMer2 algorithms and proce- anisotropic sampling during imaging (resolution in x-y plane was ten times resolution in z direc-910 tion). Anisotropic sampling generates a stair-step effect in the rendering (Figure Supplement 1A). 911 Initial vertex decimation was designed to generate meshes containing 100,000 -300,000 vertices 912 and reduced time to perform subsequent processing. Experimentation revealed this size range to 913 be the minimum that preserved geometry upon visual inspection. Next, twenty iterations of angle-914 weighted smoothing (AWS) were applied, which generated nearly equilateral triangles for the mesh 915 faces (Figure Supplement 1B). This geometry is a characteristic of a well-conditioned mesh, which annotation also allowed us to perform manipulations that removed specific parts of the original 987 reconstruction. 988 We then compared the original SBEM mesh files' surface area representations with those of the 989 3D geometry HOC files. The mesh represented the cell surface at a high resolution that captured 990 membrane crenelations, even after reducing the mesh density with GAMer2 (Lee et al., 2020b)        Otherwise, each cell was simulated using its own reconstructed axon. The first column (Soma Voltage) shows the somatic voltage for one trial for a stimulus at the characteristic frequency at 30 dB SPL. The stimulus starts after 50 ms and is 100 ms in duration. The PSTH column shows the spike rate as a function of time averaged over 100 repetitions of the tone pip, with 0.5 ms bins.
The (FSL/SSL) column shows the first spike latency distribution (FSL, blue) and second spike latency distribution (SSL, red) ; text shows the mean and SD of the FSL and SSL. The rightmost column plots the coefficient of variation (CV) of interspike intervals corrected for a 0.7 ms refractory period (CV').
. Intervals beginning less than 25 ms before the end of the stimulus were not included to minimize end effects. The CV' value is indicated to the right of each plot. All CV' values fall in the range of 0.3-0.7 reported for mouse primary-like neurons (Roos and May, 2012). The bottom row of plots shows the stimulus waveform timing for each column (blue).